1. Technical Field
The present disclosure relates to the field of global navigation satellite systems.
2. Description of the Related Art
As it is known, in order to compute one's position, a GNNS (global navigation satellite system) receiver, for example a GPS (Global Positioning System), receives properly formatted electromagnetic signals transmitted by a constellation of satellites orbiting the earth. While in theory determining location using GPS satellites is a simple process of triangulation, the reality is much more complex. First, the GPS receiver needs to find and “lock” onto enough satellites to be able to calculate its location, a process called acquisition. To calculate accurate position, however, the GPS receiver needs to know where each of these GPS satellites is in the sky with a very high degree of accuracy.
Every satellite takes 30 seconds to broadcast its precise location, and the GPS receiver is able to download these data from each satellite it needs for a fix (i.e. the computed user's position). These data, named ephemeris, describe a limited arc of orbit and are typically valid only for 2 to 3 hours. If anything interrupts the signal while receiving these data, such as a building or tree, the receiver has to wait another 30 seconds to completely download the data from the satellite.
In real-world conditions, where the GPS receiver is usually moving, it can take up to several minutes to obtain all the data the receiver needs to perform its calculations and obtain a fix, resulting in a long period with a great deal of location uncertainty before navigation can begin.
One possibility to mitigate the above problem is to autonomously generate internally to the receiver (i.e. the so called Portable Navigation Device, PND) the prediction of the satellite orbit on the basis of past downloaded ephemerides stored in the receiver memory. The autonomous satellite orbit prediction is becoming an important feature of a GNNS receiver.
The orbit of each satellite can be estimated by solving a classical celestial mechanics problem with an adequate level of knowledge about the overall forces (gravitational and non-gravitational) acting on the satellite and the so called Initial Condition (IC), meaning a satellite's position and velocity at a given time instant are available from present/past observations.
In theory a “perfect” knowledge (infinite precision) of the IC would be required to correctly solve the celestial mechanics problem. Any error in the initial conditions would generate an increasing in time position/velocity error. In practice only an initial condition with limited accuracy is available from a downloaded ephemeris. This is particularly true for the velocity. In addition to that it must be said that even the actual used transformation between ECEF (Earth Centered Earth Fixed) coordinates and the ECI (Earth Centered Inertial) coordinates might affect the accuracy of the initial condition value.
The transformation between ECEF and ECI coordinate systems includes in theory a number of different physical effects, the so called precession, nutation, polar motion effects and sidereal time calculation. For practical reasons, an autonomous system can only model all these effects with limited accuracy. The “true” data are in fact monitored and measured by the International Earth Rotation Service—IERS—which makes them available by means of periodic broadcasted bulletins. The consequence is that an implementable method for satellite orbit estimation includes a specific technique for the Initial Conditions Estimation.
Moreover, due to the limited computational capability of an embedded system, generally the implemented force models are only a limited subset of all the forces acting on an earth orbiting GNNS satellite. An exhaustive representation of the complete force models would be prohibitive for whatever commercial portable device. In addition to that there are forces which are known only to a limited level of accuracy. The consequence of these force models' inaccuracies is that the predicted satellite orbit will be affected by a position error generally growing in time (diverging error).